Service Chain and Virtual Network Embeddings: Approximations using Randomized Rounding

TL;DR

This paper introduces the first polynomial-time approximation algorithms for service chain embedding problems in SDN and NFV, using an innovative extension of linear programming and randomized rounding techniques, applicable to complex service graphs.

Contribution

It presents novel polynomial-time approximation algorithms for offline service chain embedding, extending classic LP and randomized rounding methods to complex service graphs.

Findings

First polynomial-time algorithms for service chain embedding

Extension of LP and randomized rounding to complex graphs

Applicable to service graphs with cycles or sub-chains

Abstract

The SDN and NFV paradigms enable novel network services which can be realized and embedded in a flexible and rapid manner. For example, SDN can be used to flexibly steer traffic from a source to a destination through a sequence of virtualized middleboxes, in order to realize so-called service chains. The service chain embedding problem consists of three tasks: admission control, finding suitable locations to allocate the virtualized middleboxes and computing corresponding routing paths. This paper considers the offline batch embedding of multiple service chains. Concretely, we consider the objectives of maximizing the profit by embedding an optimal subset of requests or minimizing the costs when all requests need to be embedded. Interestingly, while the service chain embedding problem has recently received much attention, so far, only non- polynomial time algorithms (based on integer programming) as well as heuristics (which do not provide any formal guarantees) are known. This paper presents the first polynomial time service chain approximation algorithms both for the case with admission and without admission control. Our algorithm is based on a novel extension of the classic linear programming and randomized rounding technique, which may be of independent interest. In particular, we show that our approach can also be extended to more complex service graphs, containing cycles or sub-chains, hence also providing new insights into the classic virtual network embedding problem.